A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems

Details A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems

2010-12-22

arxiv.org/abs/1012.5089v1

Mathematics

Numerical Analysis

10 pages

Scientific paper

We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral identity that defines the generalized solution. These estimates depend on neither special properties of the exact solution nor its approximation, and involve only global constants coming from embedding inequalities. The estimates are first derived for functions in the corresponding energy space, and then possible extensions to classes of piecewise continuous approximations are discussed.

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